27 April 2012 GeometryWarm Up

Check your Homework- “why did the mural…”HOMEWORK DUE TUESDAY: pg. 645: 1 - 20HOMEWORK DUE TUESDAY: pg. 645: 1 - 20

ObjectiveStudents will use

sine, cosine and tangent ratios to solve problems.

Students will take notes and solve problems.

You are on a boat tour around a tropical island. You see a man at the top of a cliff, diving into the water below. You know that your boat is 500 feet from the base of the cliff (your tour guide tells you) and you estimate that the angle that you look up to the top of the cliff is 30⁰ from horizontal. How high is the cliff?

Right Triangle Vocabularyhypotenuse- the longest sideleg adjacent- the side that is not the hypotenuse that helps form the angle; adjacent means “next to”leg opposite- the side that does not help form the angle; side “across” the triangle

Hypotenuse

ANGLE

Ad

jace

nt

Opposite

Sine, Cosine and Tangent are special ratios defined as follows:

SOH CAH TOA SOH CAH TOA Sine = “sin” =

Cosine = “cos” =

Tangent = “tan” =

MEMORIZE

THESE!!

WRITEWRITETHESE THESE DOWNDOWN

solving equations with trig functions

1) Strategy– rewrite the trig function as a decimal and solve for the unknown value ex: sin 42⁰ ≈ 0.6691

0.6691 =

20 (0.6691) = x x = 13. 3826

sin 4220

x

20

x

solving equations with trigfunctions

2)– remember sinϴ, cosϴ, tanϴ are RATIOSYOU CAN NOT DIVIDE the angle measure to simplify!!!

STRATEGY– use parenthesis to help you remember!

20 (sin 42⁰) = x multiply both sides by 20 20 (0.6691) = x use calculator x = 13.2826

sin 30sin

30

sin 4220

x

Solve for x. Round to the nearest 1000th.

1. 2.

3. 4.

5. 6.

sin8432

x 41

cos62x

tan 39125

x sin 42

45

x

54cos67

x 2

cos3515

x

How do you know which ratio to use?

1) Identify H, A and O.2) What information do you have? What

information do you need to find?3) Use the trig ratio with “have/need” sides.

DO Handout- TRIG Worksheet 3- Calculating Sides

debrief

Why do the trig ratios remain equivalent for any acute angle, no matter how big the triangle?

How do you know which trig function to usewhen solving trig problems?